Every words stands for unique digit that makes the arithmetic equation true

SEVEN + SEVEN + SIX = TWENTY.

What are the digits ?

I am lying and I always lie. Tell me whether I am lying or telling the truth.

It belongs to you, but other people use it more than you do. What is it?

You are provided with a grid (as shown in the picture). Can you fill the squares with numbers 1-8 in a manner that none of the two consecutive numbers are placed next to each other in any direction (vertically, horizontally or diagonally?)

A word I know has six letters it contains, remove one letter and 12 remain. What is it?

What begins with T, ends with T, and has T in it?

A doctor and a boy were fishing. The boy was the doctor’s son, but the doctor was not the boy’s father. Who was the doctor?

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different. How do you measure 45 minutes?

A large container is kept in open under the rain. Every passing hour, the water collected inside the container becomes double what it was.

In ten hours, the container is filled completely. Can you calculate how long would it have taken to be filled in half?

A few friends are enjoying their sea voyage in a boat full of apples. On the way, they felt hungry and thus decided to eat the apples. Together, they ate two dozen of apples. When they have eaten the apples, will there be any change in the water level?